CN103530523B - Child linguistic competence development evaluation modeling method - Google Patents

Abstract

The present invention relates to Language Processing field, specifically, relate to a kind of child linguistic competence development evaluation modeling method, child linguistic competence development evaluation modeling method according to the present invention, first, set up comparable child mandarin language and the data base of related cognitive ability development, then use hierarchical linear model to analyze ontogenetic development trend, use latent growth mixed model to analyze different development classifications.The child linguistic competence development evaluation modeling method of the present invention and child linguistic competence development evaluation system are for child language and related cognitive capability evaluation, prediction in early days, the Early Identification of language reading development high risk child and intervention, promote the great significance of Chinese Children linguistic competence.

Description

Child linguistic competence development evaluation modeling method

Technical field

The present invention relates to Language Processing field, in particular it relates to a kind of child linguistic competence development evaluation modeling method.

Background technology

Language is the main tool of interpersonal communication, knowledge learning, individual linguistic competence, especially reading ability, Becoming school work development and the important foundation of occupational success of people in modern society, language development may affect people in early days All one's life.Child Development was studied it has been proved that the preschool period being children physiology and developing rapidly, was also that child learns Practise and psychological development the fastest period, and degree of its development greatly affected by external environment residing for child, The research of early education to be paid close attention to and to find the method promoting that child's individuality is all-round developing.

In the past few decades, developed country has been developed by numerous studies and learns front to child and go to school in the world After language, reading and the evaluation tool of related cognitive ability development, establish the developmental norm of children in different ages. The important function of these norms is the linguistic competence that can evaluate individual child position in its same age section child Put.These are checked and examined and are particularly useful to solve the problem that preschooler language development falls behind, and are also advantageous for reducing child The risk of reading disorder after going to school.Such as, in the society of various language, suffer from that language development is slow, audition barrier Hinder thus affect reading, the child of exchange accounts for the 5-7% of school-age children.Have been developed in the world and extensively answered For clinic, medical science, the purpose of research, for checking and examining the language development pattern of baby, child, preschool children, Differentiate the test of autism, developmental retardation, dysphonia, hearing defect, aphasis etc..Test based on these The child set up divides age norm, progress curve to promote in early days to check and examine and carrying out of intervening, and promotes sending out of child Exhibition and the function of family, and bring long-term benefit for society.

Owing to Chinese and phonetic language exist greatest differences, the norm based on western alphabetic writing can not directly be answered For or simple inference to the Chinese Children using Chinese written language.Therefore, it is necessary to design a set of the most effective Chinese Children language development norm and progress curve system, may be used for health care costs in community system, kindergarten education With in primary school education system, thus realize the dynamic tracing of language development of children and early prediction.Achievement will be for Child language and related cognitive capability evaluation, prediction in early days, the Early Identification of language reading development high risk child is with dry In advance, the great significance of Chinese Children linguistic competence is promoted.

Summary of the invention

It is an object of the invention to provide a kind of child linguistic competence development evaluation modeling method.

Child linguistic competence development evaluation modeling method according to the present invention,

(1) comparable child mandarin language and the data base of related cognitive ability development are set up:

According to child age feature and Chinese feature, design is suitable for language and the survey of related cognitive ability of all ages and classes Test task, child is carried out intelligence, linguistic competence, basic cognitive ability and alpha testing, existing in a large number The data of different nature collected on child's multiple development time point carry out clearing up and system finishing, form child mandarin Language and the data base of related cognitive ability development；

(2) use hierarchical linear model analysis ontogenetic development trend:

y_ti=Λ_tη_i+e_ti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual；Λ_tRepresent the load relevant with the time Lotus matrix；η_iRepresenting the latent factor relevant with development, its average describes overall development trend, and variance describes Difference between individuality；e_tiFor the random error of corresponding individual appointment time,

In hierarchical linear model, by definition Λ_tMatrix so that η_iIn latent variable there is different containing Justice:

For the latent factor η relevant with development_i, investigate the personal feature impact on Characteristics of Development, it may be assumed that

η_i=β₀+β₁X_i+U_i

Wherein, β₀Represent at predictor variable X_iWhen being zero, the average level of the development factor, β₁Represent predictor variable X_i Impact on the development factor, U_iFor residual error, obeying average is the multivariate normal distributions of zero；

(3) the potential classification of child linguistic competence development is judged:

Using latent growth mixed model to analyze different development classifications, its model representation is:

y_kti=Λ_ktη_ki+ε_kti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual, k=1,2 ... and, K represents potential Exhibition classification, Λ_ktRepresent the loading matrix that kth group is relevant with the time, be used for representing development trend feature；η_kiRepresent the The latent factor that k group is relevant with development, its average describes the development trend that kth group is overall, and variance describes kth Difference between group individuality；ε_ktiFor the kth group random error that totally middle specified individual is corresponding with the time of appointment, diving In variable mixing model of growth, by definition Λ_ktMatrix so that η_kiIn latent variable there is different implications.

According to the detailed description of the invention of the present invention, described child linguistic competence development evaluation modeling method includes following step Rapid:

(1) comparable childrenese and the data base of related cognitive ability development are set up:

Establishment be suitable for test 3-12 year the childrenese ability of Chinese, the language that reading can be predicted and cognitive competence, And the various tests of literacy.Before learning, test is main based on oral test, increases more written survey after Test.The most the task of checking and examining of relative maturity has:

1, language aptitude test: spoken vocabulary test, syntax comprehension test,

2, basic cognitive ability test: phonetic awareness, name speed test, morpheme consciousness, orthography consciousness,

3, alpha testing: Chinese Character Recognition, sentence smoothness are read, vocabulary smoothness is read, reading understands, dictation Test,

According to child age feature and Chinese feature, design is suitable for language and the survey of related cognitive ability of all ages and classes Test task, once a year, child is carried out intelligence, linguistic competence, basic cognitive ability and alpha testing. If all ages and classes uses test instrument variant, on test design, reply all ages and classes arranges and jointly inscribes to enter The equivalent link in row later stage；Use time series research design, collect the data of at least three time point；A large amount of The data of different nature collected on child's multiple development time point carry out clearing up and system finishing, form child's Chinese Language language and the basic database of related cognitive ability development.

(2) hierarchical linear model is used to judge ontogenetic development trend:

y_ti=Λ_tη_i+e_ti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual；Λ_tRepresent the load relevant with the time Lotus matrix；η_iRepresenting the latent factor relevant with development, its average describes overall development trend, and variance describes Difference between individuality；e_tiRandom error for the corresponding individual appointment time.

In latent variable model of growth, by definition Λ_tMatrix so that η_iIn latent variable there is different implications, Following common model can illustrate.

For the latent factor η relevant with development_i, the personal feature impact on Characteristics of Development can be investigated, it may be assumed that

η_i=β₀+β₁X_i+U_i

Wherein, β₀Represent at predictor variable X_iWhen being zero, the average level of the development factor, β₁Represent predictor variable X_i Impact on the development factor, U_iFor residual error, obeying average is the multivariate normal distributions of zero.

That wherein commonly uses has:

(1) development of linear trend

Can define in above-mentioned modelWithRepresent linear model.Wherein π_0iWith π_1iRepresenting intercept and the slope of the growth of i-th individuality respectively, intercept latent variable represents that original state, language speciality are sent out The average level of exhibition, the slope latent variable representation language speciality speed of development.Intercept and slope in superincumbent model Being the stochastic variable with individuality change, the model not containing individual aspect predictor variable can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

β₀₀Represent the estimated value of intercept meansigma methods, describe the average level of language speciality original state；β₁₀Represent tiltedly The estimated value of rate meansigma methods, describes the time dependent general trend of language speciality.Random partial u_0iAt the beginning of describing Difference between beginning level individuality, its variance is the biggest, describes the difference between individuality the biggest；u_1iDescribe level The difference of development speed between individuality, its variance is the biggest, describes the development speed difference between individuality the biggest.As Really there is significant difference in the development trend between individuality, it is also possible to by the latent variable model of growth with predictor variable Analyze the reason causing ontogenetic development speed there are differences, i.e. by adding the variable of individual aspect, such as the intelligence of child Force level, describes the factor affecting ontogenetic development, can be expressed as:

π_0i=β₀₀+β₀₁Z_i+u_0i

π_1i=β₁₀++β₁₁Z_i+u_1i

Wherein Z_iFor personal feature variable, β₀₁Represent personal feature Z_iImpact on initial level, β₁₁Represent individuality Characteristic Z_iImpact on development speed.

(2) non-linear development trend

The development of some feature of linguistic competence is not development of linear trend, needs to define nonlinear model in reality The development characteristic of linguistic competence is described, can be by using the nonlinear development trend of polynomial, as led to Cross definition

Define secondary growth curve.

Wherein π_0i、π_1iAnd π_2iRepresent intercept latent variable, slope latent variable and the slope that i-th individuality increases respectively Change latent variable, is stochastic variable, can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

Wherein π_0iAnd π_1iThe implication represented is identical with linear model, π_2iRepresent the change of development speed.Such as β₁₀More than zero, β₂₀Represent that more than zero development speed is increasingly faster, β₂₀Represent that less than zero development speed is more and more slower.

(3) Multi stage development model

The development of some feature of linguistic competence there may be different developmental stage, as there is obvious turning point, and psychology This turning point is understood in research to how improving its development have great importance.Can based on latent variable model, Define different developmental stage as definition can be passed through

Define the model of growth that there are two developmental stage.

Wherein π_0i、π_1iAnd π_2iRepresent that the intercept latent variable of i-th individuality, the speed of first stage growth are dived respectively The speed latent variable that variable and second stage increase, can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

For β₁₀More than β₂₀Represent that the development speed of first stage is faster than second stage, otherwise then represent the first stage Development speed is slower than second stage.

(3) the potential classification of child linguistic competence development is judged,

Use latent growth mixed model can inquire into consider whether while development trend to there may be different Development classification, the development trend of these classifications there may be difference, and its model can be expressed as:

y_kti=Λ_ktη_ki+ε_kti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual, k=1,2 ... and, K represents potential Development classification.Λ_ktRepresent the loading matrix that kth group is relevant with the time, be used for representing development trend feature；η_kiTable Showing the latent factor that kth group is relevant with development, its average describes the development trend that kth group is overall, and variance is retouched State the difference between kth group individuality；ε_ktiFor kth group totally in specified individual and appointment time corresponding random Error.

In latent variable model of growth, by definition Λ_ktMatrix so that η_kiIn latent variable there is different implications, Similar with hierarchical linear model.

It is also conceivable to personal feature x_i(such as level of intelligence) is on development trend and the impact of development classification, model Can be expressed as:

η_ki=β_k0+β_k1x_i+u_ki

Wherein β_k0Represent and controlling x_iUnder conditions of, the development factor η of kth group_kiAverage；β_k1Represent kth group, Independent variable x_iTo the development factor η_kiImpact；u_kiThe residual vector of table kth group, its variance illustrates and considers x_i's Difference after impact, between kth group individuality.

Class (C) represents a potential classified variable, i.e. describes classified variable (the Trajectory class of change classification Variable), it is used for describing variation tendency classification that may be present.

The present invention investigate further covariant to potential classification C (k=1,2 ..., K) impact, due to dependent variable for point Class variable, can use Logistic to return the impact on covariant and be analyzed:

$P(C_i=k|x_i)=\frac{e^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}{\underset{s=1}{\overset{K}{\Σ}}{e}^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}$

With last class K class for reference to class, kth (k=1,2 ... K-1) right with K class probability of happening ratio Number is:

$log\left(\frac{P(C_i=k|x_i)}{P(C_i=K|x_i)}\right)=P(C_i=k|x_i)-P(C_i=K|x_i)={\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i$

Therefore β_1kRepresenting that covariant often increases a unit, kth class is relative to the increase of K class logarithm ratio.

Accompanying drawing explanation

Fig. 1 data analysis schematic flow sheet；

Fig. 2 hierarchical linear model schematic diagram；

Fig. 3 latent growth mixed model schematic diagram.

Detailed description of the invention

Embodiment 1

(1) comparable childrenese and the data base of related cognitive ability development are set up:

Establishment be suitable for test 3-12 year the childrenese ability of Chinese, the language that reading can be predicted and cognitive competence, And the various tests of literacy.Before learning, test is main based on oral test, increases more written survey after Test.The most the task of checking and examining of relative maturity has:

1, language aptitude test: spoken vocabulary test, syntax comprehension test,

2, basic cognitive ability test: phonetic awareness, name speed test, morpheme consciousness, orthography consciousness,

3, alpha testing: Chinese Character Recognition, sentence smoothness are read, vocabulary smoothness is read, reading understands, dictation Test,

According to child age feature and Chinese feature, design is suitable for language and the survey of related cognitive ability of all ages and classes Test task, once a year, child is carried out intelligence, linguistic competence, basic cognitive ability and alpha testing. If all ages and classes uses test instrument variant, on test design, reply all ages and classes arranges and jointly inscribes to enter The equivalent link in row later stage；Use time series research design, collect the data of at least three time point；A large amount of The data of different nature collected on child's multiple development time point carry out clearing up and system finishing, form child's Chinese Language language and the basic database of related cognitive ability development.

(2) hierarchical linear model is used to judge ontogenetic development trend:

y_ti=Λ_tη_i+e_ti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual；Λ_tRepresent the load relevant with the time Lotus matrix；η_iRepresenting the latent factor relevant with development, its average describes overall development trend, and variance describes Difference between individuality；e_tiRandom error for the corresponding individual appointment time.

In latent variable model of growth, by definition Λ_tMatrix so that η_iIn latent variable there is different implications, Following common model can illustrate.

For the latent factor η relevant with development_i, the personal feature impact on Characteristics of Development can be investigated, it may be assumed that

η_i=β₀+β₁X_i+U_i

Wherein, β₀Represent at predictor variable X_iWhen being zero, the average level of the development factor, β₁Represent predictor variable X_i Impact on the development factor, U_iFor residual error, obeying average is the multivariate normal distributions of zero.

That wherein commonly uses has:

(1) development of linear trend

Can define in above-mentioned modelWithRepresent linear model.Wherein π_0iWith π_1iRepresenting intercept and the slope of the growth of i-th individuality respectively, intercept latent variable represents that original state, language speciality are sent out The average level of exhibition, the slope latent variable representation language speciality speed of development.Intercept and slope in superincumbent model Being the stochastic variable with individuality change, the model not containing individual aspect predictor variable can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

β₀₀Represent the estimated value of intercept meansigma methods, describe the average level of language speciality original state；β₁₀Represent tiltedly The estimated value of rate meansigma methods, describes the time dependent general trend of language speciality.Random partial u_0iAt the beginning of describing Difference between beginning level individuality, its variance is the biggest, describes the difference between individuality the biggest；u_1iDescribe level The difference of development speed between individuality, its variance is the biggest, describes the development speed difference between individuality the biggest.As Really there is significant difference in the development trend between individuality, it is also possible to by the latent variable model of growth with predictor variable Analyze the reason causing ontogenetic development speed there are differences, i.e. by adding the variable of individual aspect, such as the intelligence of child Force level, describes the factor affecting ontogenetic development, can be expressed as:

π_0i=β₀₀+β₀₁Z_i+u_0i

π_1i=β₁₀++β₁₁Z_i+u_1i

Wherein Z_iFor personal feature variable, β₀₁Represent personal feature Z_iImpact on initial level, β₁₁Represent individuality Characteristic Z_iImpact on development speed.

(2) non-linear development trend

The development of some feature of linguistic competence is not development of linear trend, needs to define nonlinear model in reality The development characteristic of linguistic competence is described, can be by using the nonlinear development trend of polynomial, as led to Cross definition

Define secondary growth curve.

Wherein π_0i、π_1iAnd π_2iRepresent intercept latent variable, slope latent variable and the slope that i-th individuality increases respectively Change latent variable, is stochastic variable, can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

Wherein π_0iAnd π_1iThe implication represented is identical with linear model, π_2iRepresent the change of development speed.Such as β₁₀More than zero, β₂₀Represent that more than zero development speed is increasingly faster, β₂₀Represent that less than zero development speed is more and more slower.

(3) Multi stage development model

The development of some feature of linguistic competence there may be different developmental stage, as there is obvious turning point, and psychology This turning point is understood in research to how improving its development have great importance.Can based on latent variable model, Define different developmental stage as definition can be passed through

Define the model of growth that there are two developmental stage.

Wherein π_0i、π_1iAnd π_2iRepresent that the intercept latent variable of i-th individuality, the speed of first stage growth are dived respectively The speed latent variable that variable and second stage increase, can be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

For β₁₀More than β₂₀Represent that the development speed of first stage is faster than second stage, otherwise then represent the first stage Development speed is slower than second stage.

(3) the potential classification of child linguistic competence development is judged,

Use latent growth mixed model can inquire into consider whether while development trend to there may be different Development classification, the development trend of these classifications there may be difference, and its model can be expressed as:

y_kti=Λ_ktη_ki+ε_kti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual, k=1,2 ... and, K represents potential Development classification.Λ_ktRepresent the loading matrix that kth group is relevant with the time, be used for representing development trend feature；η_kiTable Showing the latent factor that kth group is relevant with development, its average describes the development trend that kth group is overall, and variance is retouched State the difference between kth group individuality；ε_ktiFor kth group totally in specified individual and appointment time corresponding random Error.

In latent variable model of growth, by definition Λ_ktMatrix so that η_kiIn latent variable there is different implications, Similar with hierarchical linear model.

It is also conceivable to personal feature x_i(such as level of intelligence) is on development trend and the impact of development classification, model Can be expressed as:

η_ki=β_k0+β_k1x_i+u_ki

Wherein β_k0Represent and controlling x_iUnder conditions of, the development factor η of kth group_kiAverage；β_k1Represent kth group, Independent variable x_iTo the development factor η_kiImpact；u_kiThe residual vector of table kth group, its variance illustrates and considers x_i's Difference after impact, between kth group individuality.

Class (C) represents a potential classified variable, i.e. describes classified variable (the Trajectory class of change classification Variable), it is used for describing variation tendency classification that may be present.

The present invention investigate further covariant to potential classification C (k=1,2 ..., K) impact, due to dependent variable for point Class variable, can use Logistic to return the impact on covariant and be analyzed:

$P(C_i=k|x_i)=\frac{e^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}{\underset{s=1}{\overset{K}{\Σ}}{e}^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}$

With last class K class for reference to class, kth (k=1,2 ... K-1) right with K class probability of happening ratio Number is:

$log\left(\frac{P(C_i=k|x_i)}{P(C_i=K|x_i)}\right)=P(C_i=k|x_i)-P(C_i=K|x_i)={\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i$

Therefore β_1kRepresenting that covariant often increases a unit, kth class is relative to the increase of K class logarithm ratio.

The step of child linguistic competence development evaluation modeling method below as a example by Mplus analysis process, will be described.

Analysis below is carried out for the data of entitled " reading development model.dat ", each variable name implication As follows: P1-P4 is the tone testing score of the 1st to the 4th testing point.

Example 1. phonetic awareness development trend describes.(hierarchical linear model)

The subpopulation of example 2. speech capability development trend.(latent growth mixed model)

Claims (3)

1. child linguistic competence development evaluation modeling method, it is characterised in that said method comprising the steps of:

(1) comparable child mandarin language and the data base of related cognitive ability development are set up:

According to child age feature and Chinese feature, design is suitable for language and the survey of related cognitive ability of all ages and classes Test task, child is carried out intelligence, linguistic competence, basic cognitive ability and alpha testing, existing in a large number The data of different nature collected on child's multiple development time point carry out clearing up and system finishing, form child mandarin Language and the data base of related cognitive ability development；

(2) use hierarchical linear model analysis ontogenetic development trend:

y_ti=Λ_tη_i+e_ti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual；Λ_tRepresent the load relevant with the time Lotus matrix；η_iRepresenting the latent factor relevant with development, its average describes overall development trend, and variance describes Difference between individuality；e_tiFor the random error of corresponding individual appointment time,

In hierarchical linear model, by definition Λ_tMatrix so that η_iIn latent variable there is different containing Justice:

For the latent factor η relevant with development_i, investigate the personal feature impact on Characteristics of Development, it may be assumed that

η_i=β₀+β₁X_i+U_i

Wherein, β₀Represent at predictor variable X_iWhen being zero, the average level of the development factor, β₁Represent predictor variable X_i Impact on the development factor, U_iFor residual error, obeying average is the multivariate normal distributions of zero,

Wherein, ontogenetic development trend includes:

(1) development of linear trend

Can define in above-mentioned modelWithRepresent linear model, wherein π_0iWith π_1iRepresenting intercept and the slope of the growth of i-th individuality respectively, intercept latent variable represents that original state, language speciality are sent out The average level of exhibition, the slope latent variable representation language speciality speed of development,

In superincumbent model, intercept and slope are the stochastic variables with individuality change, do not contain individual aspect predictor variable Model be described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

β₀₀Represent the estimated value of intercept meansigma methods, describe the average level of language speciality original state,

β₁₀Represent the estimated value of slope meansigma methods, describe the time dependent general trend of language speciality,

Random partial u_0iDescribing the difference between initial level individuality, its variance is the biggest, describes the difference between individuality It is different the biggest,

u_1iDescribing the difference of development speed between level individuality, its variance is the biggest, describes the development speed between individuality Degree difference is the biggest,

If the development trend between individuality exists significant difference, divided by the latent variable model of growth with predictor variable Analysis causes the reason that ontogenetic development speed there are differences, i.e. by adding the variable of individual aspect, such as the intelligence of child Level, describes the factor affecting ontogenetic development, is expressed as:

π_0i=β₀₀+β₀₁Z_i+u_0i

π_1i=β₁₀++β₁₁Z_i+u_1i

Wherein Z_iFor personal feature variable, β₀₁Represent personal feature Z_iImpact on initial level, β₁₁Represent individuality Characteristic Z_iImpact on development speed；

(2) non-linear development trend

Define nonlinear model to describe the development characteristic of linguistic competence, can be by using polynomial non-linear Development trend, by definition

Define secondary growth curve

Wherein π_0i、π_1iAnd π_2iRepresent intercept latent variable, slope latent variable and the slope that i-th individuality increases respectively Change latent variable, is stochastic variable, is described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

Wherein π_0iAnd π_1iThe implication represented is identical with linear model, π_2iRepresent the change of development speed；

(3) Multi stage development model

Based on latent variable model, define different developmental stage, by definition

Define the model of growth that there are two developmental stage

Wherein π_0i、π_1iAnd π_2iRepresent that the intercept latent variable of i-th individuality, the speed of first stage growth are dived respectively The speed latent variable that variable and second stage increase, is described as:

π_0i=β₀₀+u_0i

π_1i=β₁₀+u_1i

π_2i=β₂₀+u_2i

For β₁₀More than β₂₀Represent that the development speed of first stage is faster than second stage, otherwise then represent the first stage Development speed is slower than second stage；

(3) the potential classification of child linguistic competence development is judged:

Using latent growth mixed model to analyze different development classifications, its model representation is:

y_kti=Λ_ktη_ki+ε_kti

Wherein t=1,2 ..., T express time, i=1,2 ..., n represents individual, k=1,2 ... and, K represents potential Development classification, Λ_ktRepresent the loading matrix that kth group is relevant with the time, be used for representing development trend feature；η_kiTable Showing the latent factor that kth group is relevant with development, its average describes the development trend that kth group is overall, and variance is retouched State the difference between kth group individuality；ε_ktiFor kth group totally in specified individual and appointment time corresponding random Error, in latent growth mixed model, by definition Λ_ktMatrix so that η_kiIn latent variable have not Same implication.

Child linguistic competence development evaluation modeling method the most according to claim 1, it is characterised in that enter one Step considers personal feature x_iOn development trend and the impact of the potential classification of child linguistic competence development, model representation is:

η_ki=β_k0+β_k1x_i+u_ki

Wherein β_k0Represent and controlling x_iUnder conditions of, the development factor η of kth group_kiAverage；β_k1Represent kth group, Independent variable x_iTo the development factor η_kiImpact；u_kiThe residual vector of table kth group, its variance illustrates and considers x_i's Difference after impact, between kth group individuality.

Child linguistic competence development evaluation modeling method the most according to claim 1, it is characterised in that with latent Describe the classified variable of change classification at classified variable C, be used for describing variation tendency classification that may be present,

Investigate further covariant to potential classified variable C (k=1,2 ..., K) impact:

$P(C_i=k|x_i)=\frac{e^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}{\underset{s=1}{\overset{K}{\mathrm{\Σ}}}{e}^{{\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i}}$

With last class K class for reference to class, kth (k=1,2 ... K-1) right with K class probability of happening ratio Number is:

$log\left(\frac{P(C_i=k|x_i)}{P(C_i=K|x_i)}\right)=P(C_i=k|x_i)-P(C_i=K|x_i)={\mathrm{\β}}_{0k}+{\mathrm{\β}}_{1k}{x}_i$

Therefore β_1kRepresenting that covariant often increases a unit, kth class is relative to the increase of K class logarithm ratio.